Explanation Given: 3 x ² − 10 x y + 3 y ² − 3 = 0 Formula used: To transform A x ² + B x y + C y ² + D x + E y + F = 0 , B ≠ 0 into an equation in x ' and y ' without an x ′ y ′ -term, rotate the axes through an angle θ that satisfies the equation Cot ( 2 θ ) = A − C B . x = x ′ cos θ − y ′ sin θ ; y = x ′ sin θ + y ′ cos θ Calculation: Consider the given equation, 3 x ² − 10 x y + 3 y ² − 3 = 0 . A = 3 , B = − 10 and C = 3 ; Cot ( 2 θ ) = A − C B ; 3 − 3 −

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

4th Edition

ISBN: 9780134686974

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

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Question

Chapter 9.5, Problem 24AYU

To determine

The appropriate rotation formula to use so that new equation contains no $x y$ term: $3 x ² - 10 x y + 3 y ² - 3 = 0$ .

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Chapter 9.5, Problem 23AYU

Chapter 9.5, Problem 25AYU

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Chapter 9 Solutions

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

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The appropriate rotation formula to use so that new equation contains no x y term: 3 x ² − 10 x y + 3 y ² − 3 = 0 .

Solution Summary: The author explains how to determine the appropriate rotation formula to use so that new equation contains no x y term.

The appropriate rotation formula to use so that new equation contains no $x y$ term: $3 x ² - 10 x y + 3 y ² - 3 = 0$ .

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Chapter 9 Solutions

The appropriate rotation formula to use so that new equation contains no x y term: 3 x ² − 10 x y + 3 y ² − 3 = 0 .

Solution Summary: The author explains how to determine the appropriate rotation formula to use so that new equation contains no x y term.

The appropriate rotation formula to use so that new equation contains no xy term: 3x² − 10xy + 3y² − 3 = 0 .

Want to see the full answer?

Chapter 9 Solutions

The appropriate rotation formula to use so that new equation contains no $x y$ term: $3 x ² - 10 x y + 3 y ² - 3 = 0$ .